Regarding the rate of convergence for \((u_\varepsilon , P_\varepsilon )\)  in \(L^2(\Omega )\) ,
to the best of the author's knowledge, the only previous result for a bounded domain with
the Dirichlet condition was obtained by E. Marušić-Paloka and A. Mikelić
in [1]}, where a rate \(O(\varepsilon ^{1/6})\)  was established for the case \(d=2\) .
See [2]} for an earlier result for a unbounded domain \(\Omega =(0, L) \times \mathbb {R}_+\) .
We remark that for Laplace's equation and systems of linear elasticity, quantitative error estimates have been established
in [3]}, [4]}, [5]}, [6]}, [7]}.
As pointed out in [1]}, the simple cut-off argument, which seems to work well for standard elliptic
equations and systems, does not yield any convergence rate for the Stokes equations because of the incompressibility condition.
In [1]}, using a stream function from [10]},
a boundary corrector was constructed in the case \(d=2\)  to control the boundary layer
near \(\partial \Omega \)  created by the incompressibility condition.
We mention that [1]} also treated the case of nonlinear stationary Navier-Stokes equations.
